Objective(s):

1. Review graphing requirements (see IA guide: p 54 ->)
2. Determine mean, range, and absolute error
3. Learn to find "absolute error" in measurement according to the instrument used for measurement.

Today's Lesson:

• Review purpose of different graphs: pie, bar, histogram, scatterplot, line
• Use IA guide (Talbot, p54...) to make sure students complete their brought-to-class graph with all IB required elements of a graph

1. Mean is "average"
   • plot this point on graph and add error bars (see below)
2. "Error bars" on a graph can show: (1) range plus error or (2) standard deviation (SD) [we will do SD next class].
   • Range should be shown as largest and smallest value.
   • Note that upper and lower limits of range may not be same distance from mean.
   • Don't forget to add "absolute error" to the range (which pushed the range a little higher and a little lower.)
3. Absolute error
   • There are several guides for "error:" absolute, relative and %.
   • Absolute refers to error in instruments used for measuring.
   • Usually, a measurement written in significant figures implies an error of +/- 50% of smallest "increment" used to measure. Since we measure height to nearest cm, then a height of 165 cm is correct +/- 0.5 cm. Notice that in absolute error, the error quantity MAY BE beyond the measurement of significance (ie. this is not significant to 0.1 cm - see measurement). It is unclear how we can account for error smaller than our ability to measure with the instrument, but it is recorded this way nonetheless. In any case, as Merson-Davies pointed out, "variability in measurement of living organisms is often far greater than instrument error and is insignificant in many cases" ("Student Guide for Internal Assessment in Biology" by Merson-Davies, p 13, 2005). In other words, the variation in traits of your organsisms is usually much greater than the errors which your instrument permits in measuring.
     • age will be +/- 1 month (due to ignoring the actual date of birth and using only month; this keeps error under 1%)
     • height will be read as, ex. 165 cm. This implies an error of half smallest increment, which is correct: +/- 0.5 cm. Note that the error falls outside the range of significance for measurement. This is the format used in the IB (see Talbot's Student Guide to Internal Assessment-Biology on p 36.)
     • maximum lung volume from the spirometer is read to three sig digs, like 2350 cc (2.35 L). Note that since smaller increment on instrument is 100 cc, the rule of thumb would be +/- 50 cc. As a percentage this is acceptable, however, error is more correctly written here as +/- 20 cc. From reading Talbot's and Ashby Merson-Davies "internal assessment guides" for students, error seems unltimately to be a value determined by the experienced instrument user - so teach kids to read well, practice caution and report the real data!
     • student mass on this spring bathroom scale is probably no better than half the smallest increment (ie. +/- 0.5 kg) and in fact may be worse!